On a class of nonlocal problems with fractional gradient constraint

  • Assis Azevedo

    Universidade do Minho, Braga, Portugal
  • José-Francisco Rodrigues

    Universidade de Lisboa, Portugal
  • Lisa Santos

    Universidade do Minho, Braga, Portugal
On a class of nonlocal problems with fractional gradient constraint cover
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Abstract

We consider a Hilbertian and a charges approach to fractional gradient constraint problems of the type , involving the distributional fractional Riesz gradient , , extending previous results on the existence of solutions and Lagrange multipliers of these nonlocal problems.

We also prove their convergence as towards their local counterparts with the gradient constraint .